Regularity of Tensor Product Approximations to Square Integrable Functions
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We investigate first-order conditions for canonical and optimal subspace (Tucker format) tensor product approximations to square integrable functions. They reveal that the best approximation and all of its factors have the same smoothness as the approximated function itself. This is not obvious, since the approximation is performed in L2.
KeywordsTensor products Low-rank approximation Optimal subspace approximation Sobolev spaces
Mathematics Subject Classification (2000)15A69 41A46 49N60
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